Sufficient conditions for stability of linear time-delay systems with dependent delays

According to the delay property, linear time-delay (LTD) systems can be classified as LTD systems with dependent delays (LTD.DD) and LTD systems with independent delays (LTDID). This paper reveals that the stability condition for LTDID systems can be applied to LTD.DD systems, a sufficient stability condition for LTD.DD systems is derived from it, while only fewer of the LTD.DD systems can satisfy the stability condition due to the very strict limitation for the delays of the LTD.DD systems. To solve the problem, based on two-dimensional (2-D) hybrid polynomials, some sufficient conditions for stability of LTD.DD systems are proposed. Examples show that the proposed stability test algorithms are simple and valid.